Many-body Non-Hermitian Skin Effect for Multipoles: Disorder and Localization Transitions

We investigate the fate of the non-Hermitian skin effect in one-dimensional systems that conserve the dipole moment and higher moments of a global U(1) charge. The key feature of the non-Hermitian skin effect for m-pole conserving systems is the generation of an (m+1)th multipole moment, which can be seen both in eigenstates and dynamically. For example, in contrast to the conventional skin effect, where charges are anomalously localized at a single boundary, the dipole-conserving skin effect localized charges at both boundaries, in a configuration that maximizes the quadrupole moment. Looking beyond the distribution of charge, we show that entanglement entropy serves as a quantum signature of the many-body skin effect. Using these local and global probes, we argue that multipole skin effects can both enhance and forbid localization transitions in disordered systems, depending on boundary conditions.